Fish Comparisons Simple Models

Alright, so from all of this what do I know?

Speed Differences: Flow increases speed differences Ablation decreases speed differences Darkness increases speed differences Distance increases speed differences Angles around 90 degrees have a bigger difference in speed

Heading Differences: Fish are more aligned when they are around 90 degrees, slightly less in ablated fish

Synchronization: Darkness increases synchronization

NND: Darkness increases NND Flow decreases NND

Nearest Neighbor Bearing: In darkness fish are more in front or behind In flow fish are more in positioned alongside each other

Sets up the functions that will be used later

rad2deg <- function(rad) {(rad * 180) / (pi)}
deg2rad <- function(deg) {(deg * pi) / (180)}
round_any <- function(x, accuracy, f=round){f(x/ accuracy) * accuracy}
ang_mean <- function(x){rad2deg(atan(mean(sin(deg2rad(x)))/mean(cos(deg2rad(x)))))}

fold_angle_0_360_to_0_180 <- function(x){abs(abs(x-180)-180)}

fold_angle_neg_180_180_to_neg_90_90 <- function(x){ifelse(x > 90,90-abs(90-x),ifelse(x < -90, -90+abs(-90-x), x))}

min_n <- function(x,n){sort(x)[1:n]}
max_n <- function(x,n){sort(x,decreasing = TRUE)[1:n]}

Reads in the data and alters it as needed

comp_data <- read.csv("Fish_Comp_Values.csv")
comp_data <- na.omit(comp_data)

comp_data <- comp_data %>% mutate(Flow = ifelse(Flow == "0", "Flow 0", "Flow 2")) %>%
                           mutate(Ablation = ifelse(Ablation == "N", "No Ablation", "Ablated")) %>%
                           mutate(Darkness = ifelse(Darkness == "N", "Light", "Dark")) %>%
                           filter(Distance <= 4) %>%
                           filter(abs(Speed_Diff) <= 6) %>% 
                           mutate(Speed_Diff = abs(Speed_Diff)) %>%
                           mutate(fold_heading_diff = abs(fold_angle_neg_180_180_to_neg_90_90(Heading_Diff))) %>%
                           mutate(Is_Aligned = ifelse(Heading_Diff < 30, 1, 0)) %>%
                           mutate(Is_Reversed = ifelse(Heading_Diff > 150, 1, 0)) %>%
                           separate(Fish, c("Fish1", "Fish2"),sep="x") %>%
                           mutate(Flow = factor(Flow), Ablation = factor(Ablation), Darkness = factor(Darkness)) %>%
                           mutate(Flow = fct_relevel(Flow, c("Flow 0","Flow 2"))) %>%
                           mutate(Ablation = fct_relevel(Ablation, c("No Ablation","Ablated"))) %>%
                           mutate(Darkness = fct_relevel(Darkness, c("Light","Dark"))) %>%
                           mutate(rad_Angle = Angle) %>%
                           mutate(sin_Angle = sin(rad_Angle), cos_Angle = cos(rad_Angle)) %>%
                           mutate(Flow_Ablation_Darkness = factor(paste(Flow,Ablation,Darkness,sep=", ")))
                           
                           #mutate(Angle = fold_angle_0_360_to_0_180(Angle))

sum_comp_data <- comp_data %>% mutate(X_Distance = round_any(X_Distance,0.25), 
                                      Y_Distance = round_any(abs(Y_Distance),0.25)) %>%
                               group_by(Flow,Ablation,Darkness,X_Distance,Y_Distance) %>%
                               summarise(Speed_Diff = mean(Speed_Diff),
                                         Heading_Diff = ang_mean(Heading_Diff),
                                         Sync = mean(Sync),
                                         Fold_Heading_Diff = mean(fold_heading_diff),
                                         Is_Aligned = mean(Is_Aligned),
                                         Is_Reversed = mean(Is_Reversed))

`summarise()` has grouped output by 'Flow', 'Ablation', 'Darkness', 'X_Distance'. You can override using the `.groups` argument.

comp_data_switch_fish <- comp_data %>% mutate(Fish3 = Fish1) %>%
                                       mutate(Fish1 = Fish2) %>%
                                       mutate(Fish2 = Fish3) %>%
                                       select(-c(Fish3))

comp_data_NND <- bind_rows(comp_data, comp_data_switch_fish) %>% group_by(Year,Month,Day,Trial,Fish1,Tailbeat.Num) %>%
                                                                 filter(Distance == min(Distance)) %>%
                                                                 ungroup()

comp_data_near_3 <- bind_rows(comp_data, comp_data_switch_fish) %>% group_by(Year,Month,Day,Trial,Fish1,Tailbeat.Num) %>%
                                                                 slice_min(Distance, n = 3) %>%
                                                                 ungroup() %>%
                                                                 distinct(Distance, .keep_all= TRUE)

#Basic Stats

speed_anova <- aov(Speed_Diff ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_near_3)

Anova(speed_anova)

Anova Table (Type II tests)

Response: Speed_Diff
               Sum Sq   Df F value    Pr(>F)    
Flow            18.03    1 67.1684 3.222e-16 ***
Ablation         1.56    1  5.8279  0.015814 *  
Darkness         0.95    1  3.5464  0.059739 .  
Flow:Ablation    0.01    1  0.0254  0.873339    
Flow:Darkness    3.53    1 13.1677  0.000288 ***
Residuals     1203.00 4482                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

heading_anova <- aov(fold_heading_diff ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_near_3)

Anova(heading_anova)

Anova Table (Type II tests)

Response: fold_heading_diff
               Sum Sq   Df F value    Pr(>F)    
Flow            44371    1 67.3744 2.907e-16 ***
Ablation          277    1  0.4210   0.51645    
Darkness        10451    1 15.8685 6.898e-05 ***
Flow:Ablation    1978    1  3.0042   0.08312 .  
Flow:Darkness      36    1  0.0549   0.81476    
Residuals     2951752 4482                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

sync_anova <- aov(Sync ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_near_3)

Anova(sync_anova)

Anova Table (Type II tests)

Response: Sync
               Sum Sq   Df F value   Pr(>F)   
Flow            0.000    1  0.0052 0.942353   
Ablation        0.004    1  0.0568 0.811706   
Darkness        0.463    1  7.4662 0.006312 **
Flow:Ablation   0.022    1  0.3618 0.547558   
Flow:Darkness   0.204    1  3.2819 0.070117 . 
Residuals     277.923 4482                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

dist_anova <- aov(Distance ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(dist_anova)

Anova Table (Type II tests)

Response: Distance
               Sum Sq   Df  F value    Pr(>F)    
Flow             4.35    1   9.5503  0.002019 ** 
Ablation         0.15    1   0.3347  0.562954    
Darkness       102.00    1 223.9367 < 2.2e-16 ***
Flow:Ablation    0.01    1   0.0166  0.897363    
Flow:Darkness    1.86    1   4.0795  0.043503 *  
Residuals     1254.36 2754                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

angle_anova <- aov(Angle ~ Flow + Ablation + Darkness + Flow:Ablation + Flow:Darkness, data = comp_data_NND)

Anova(dist_anova)

Anova Table (Type II tests)

Response: Distance
               Sum Sq   Df  F value    Pr(>F)    
Flow             4.35    1   9.5503  0.002019 ** 
Ablation         0.15    1   0.3347  0.562954    
Darkness       102.00    1 223.9367 < 2.2e-16 ***
Flow:Ablation    0.01    1   0.0166  0.897363    
Flow:Darkness    1.86    1   4.0795  0.043503 *  
Residuals     1254.36 2754                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

ggplot(comp_data_near_3, aes(x = cos(deg2rad(Angle))))+
  geom_histogram()+
  facet_wrap(~ Flow + Ablation + Darkness)

ggplot(comp_data_near_3, aes(x = sin(deg2rad(Angle))))+
  geom_histogram()+
  facet_wrap(~ Flow + Ablation + Darkness)

ggplot(comp_data_near_3, aes(x = Flow, y = Speed_Diff, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_boxplot(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Speed Difference") +
  xlab("") +
  ylab("Speed Difference (BL/s)") +
  ylim(-0.1,2.5) +
  theme_light()

ggplot(comp_data_near_3, aes(x = Flow, y = fold_heading_diff, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_boxplot(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Heading Difference") +
  xlab("") +
  ylab("Heading Difference (Degrees)") +
  theme_light()

ggplot(comp_data_near_3, aes(x = Flow, y = Sync, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_boxplot(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Tailbeat Synchonization") +
  xlab("") +
  ylab("Syncronization") +
  theme_light()

ggplot(comp_data_near_3, aes(x = Flow, y = Distance, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_boxplot(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Nearest Neighbor Distance (NND)") +
  xlab("") +
  ylab("NND (BL)") +
  theme_light()

ggplot(comp_data_near_3, aes(x = Flow, y = Angle, fill = interaction(Ablation,Darkness,sep=", ")))+
  geom_boxplot(outlier.shape = NA) +
  guides(fill = guide_legend(title = "Condition")) +
  scale_fill_manual(values=c("#EEEEEE", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Available Senses on Nearest Neighbor Bearing") +
  xlab("") +
  ylab("Nearest Neighbor Bearing (Degrees)") +
  scale_y_continuous(breaks = c(30,60,90,120,150)) +
  theme_light()

Trying GAMs

speed_gam <- gam(Speed_Diff ~ s(Distance,Angle,by=Flow_Ablation_Darkness),
                              data = comp_data_near_3)

summary(speed_gam)

Family: gaussian 
Link function: identity 

Formula:
Speed_Diff ~ s(Distance, Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.621779   0.008037   77.37   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                                     edf Ref.df      F  p-value    
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light     2.000  2.000 44.263  < 2e-16 ***
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  2.000  2.000  3.355 0.034997 *  
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light 4.572  5.822  4.413 0.000244 ***
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     4.325  5.485  4.788 0.000154 ***
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  4.133  5.230  5.702  2.5e-05 ***
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light 2.000  2.000  8.196 0.000280 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.0396   Deviance explained = 4.37%
GCV = 0.26585  Scale est. = 0.26466   n = 4488

heading_gam <- gam(fold_heading_diff ~ s(Distance,Angle,by=Flow_Ablation_Darkness),
                              data = comp_data_near_3)

summary(heading_gam)

Family: gaussian 
Link function: identity 

Formula:
fold_heading_diff ~ s(Distance, Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  38.6811     0.4036   95.83   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                                     edf Ref.df     F p-value   
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light     7.027  9.057 2.905 0.00194 **
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  2.000  2.000 0.626 0.53461   
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light 2.000  2.000 1.010 0.36439   
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     5.536  7.091 0.940 0.47446   
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  6.922  8.829 3.047 0.00143 **
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light 2.000  2.000 0.340 0.71198   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.0113   Deviance explained = 1.69%
GCV = 670.78  Scale est. = 666.82    n = 4488

sync_gam <- gam(Sync ~ s(Distance,Angle,by=Flow_Ablation_Darkness),
                              data = comp_data_near_3)

summary(sync_gam)

Family: gaussian 
Link function: identity 

Formula:
Sync ~ s(Distance, Angle, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.540504   0.003869   139.7   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                                     edf Ref.df     F  p-value    
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, Ablated, Light     5.433  6.967 4.868 1.89e-05 ***
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  4.258  5.392 1.515   0.1816    
s(Distance,Angle):Flow_Ablation_DarknessFlow 0, No Ablation, Light 3.972  5.020 2.353   0.0381 *  
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, Ablated, Light     4.563  5.803 1.955   0.0675 .  
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  2.000  2.000 0.914   0.4010    
s(Distance,Angle):Flow_Ablation_DarknessFlow 2, No Ablation, Light 2.000  2.000 1.228   0.2929    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.0132   Deviance explained = 1.81%
GCV = 0.061633  Scale est. = 0.061314  n = 4488

Now we make some predictions for this.

d <- seq(from = 0, to = 3, by = 0.1)
a <- seq(from = 0, to = 180, by = 10)

flows <- c("Flow 0", "Flow 2")
ablation <- c("No Ablation", "Ablated")
dark <- c("Light","Dark")

predict_df <- expand.grid(Distance = d, Angle = a, Flow = flows, Ablation = ablation, Darkness = dark)

predict_df <- predict_df %>% mutate(Flow_Ablation_Darkness = factor(paste(Flow,Ablation,Darkness,sep=", "))) %>% 
                            filter(!(Ablation == "Ablated" & Darkness == 'Dark'))

predict_df <- predict_df %>% mutate(pred_speed_diff = predict.gam(speed_gam,predict_df),
                                    pred_heading_diff = predict.gam(heading_gam,predict_df),
                                    pred_sync = predict.gam(sync_gam,predict_df))

predict_df <- predict_df %>% group_by(Distance,Flow,Ablation,Darkness) %>%
                             mutate(mean_Speed_Distance = mean(pred_speed_diff), sd_Speed_Distance = sd(pred_speed_diff),
                                    mean_Heading_Distance = mean(pred_heading_diff), sd_Heading_Distance = sd(pred_heading_diff),
                                    mean_Sync_Distance = mean(pred_sync), sd_Sync_Distance = sd(pred_sync)) %>%
                             ungroup() %>%
                             group_by(Angle,Flow,Ablation,Darkness) %>%
                             mutate(mean_Speed_Angle = mean(pred_speed_diff), sd_Speed_Angle = sd(pred_speed_diff),
                                    mean_Heading_Angle = mean(pred_heading_diff), sd_Heading_Angle = sd(pred_heading_diff),
                                    mean_Sync_Angle = mean(pred_sync), sd_Sync_Angle = sd(pred_sync)) %>%
                             ungroup()

And now we graph those?

ggplot(predict_df, aes(x = Distance, y = mean_Speed_Distance, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=" "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Distance, y = pred_speed_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Speed_Distance-sd_Speed_Distance, ymax = mean_Speed_Distance+sd_Speed_Distance),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Distance and Senses on Speed Difference") +
  xlab("Distance (BL)") +
  ylab("Speed Difference (BL/s)") +
  ylim(0,1.5) +
  theme_light()

ggplot(predict_df, aes(x = Distance, y = mean_Heading_Distance, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Distance, y = pred_heading_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Heading_Distance-sd_Heading_Distance, ymax = mean_Heading_Distance+sd_Heading_Distance),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Distance and Senses on Heading Difference") +
  xlab("Distance (BL)") +
  ylab("Heading Difference (Degrees)") +
  ylim(0,50) +
  theme_light()

ggplot(predict_df, aes(x = Distance, y = mean_Sync_Distance, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  #geom_point(data=predict_df, aes(x = Distance, y = pred_sync, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Sync_Distance-sd_Sync_Distance, ymax = mean_Sync_Distance+sd_Sync_Distance),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Distance and Senses on Synchonization") +
  xlab("Distance (BL)") +
  ylab("Synchonization") +
  ylim(0,1)+
  theme_light()

ggplot(predict_df, aes(x = Angle, y = mean_Speed_Angle, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  geom_point(data=predict_df, aes(x = Angle, y = pred_speed_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Speed_Angle-sd_Speed_Angle, ymax = mean_Speed_Angle+sd_Speed_Angle),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Bearing and Senses on Speed Difference") +
  xlab("Bearing (Degrees)") +
  ylab("Speed Difference (BL/s)") +
  ylim(0,1.5) +
  theme_light()

ggplot(predict_df, aes(x = Angle, y = mean_Heading_Angle, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  geom_point(data=predict_df, aes(x = Angle, y = pred_heading_diff, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Heading_Angle-sd_Heading_Angle, ymax = mean_Heading_Angle+sd_Heading_Angle),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Bearing and Senses on Heading Difference") +
  xlab("Angle (Degrees)") +
  ylab("Heading Difference (Degrees)") +
  ylim(0,50) +
  theme_light()

ggplot(predict_df, aes(x = Angle, y = mean_Sync_Angle, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  geom_point(data=predict_df, aes(x = Angle, y = pred_sync, alpha = 0.15)) +
  geom_ribbon(aes(ymin = mean_Sync_Angle-sd_Sync_Angle, ymax = mean_Sync_Angle+sd_Sync_Angle),
              linetype = 0,
              alpha = 0.1) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Bearing and Senses on Synchonization") +
  xlab("Bearing (Degrees)") +
  ylab("Synchonization") +
  ylim(0,1)+
  theme_light()

Density vs Things

dist_bin_size <- 1
angle_bin_size <- 30

comp_data_freqs <- comp_data_near_3 %>% mutate(Dist_bin = round_any(Distance, dist_bin_size), 
                                               Angle_bin = round_any(Angle, angle_bin_size)) %>%
                                        group_by(Flow,Darkness,Ablation, Dist_bin, Angle_bin,Flow_Ablation_Darkness) %>%
                                        mutate(Count = n()) %>%
                                        ungroup() %>%
                                        group_by(Flow,Darkness,Ablation,Flow_Ablation_Darkness) %>%
                                        mutate(Freq = Count/n()) %>%
                                        ungroup() %>%
                                        group_by(Flow,Darkness,Ablation,Dist_bin,Angle_bin,Flow_Ablation_Darkness) %>%
                                        summarise(Speed_Diff = mean(Speed_Diff),
                                                  Fold_Heading_Diff = ang_mean(fold_heading_diff),
                                                  Sync = mean(Sync),
                                                  Freq = mean(Freq))

`summarise()` has grouped output by 'Flow', 'Darkness', 'Ablation', 'Dist_bin', 'Angle_bin'. You can override using the `.groups` argument.

freq_speed_glm <- glm(Speed_Diff ~ Freq*(Flow+Darkness+Ablation+Flow:Ablation+Flow:Darkness), data = comp_data_freqs)

summary(freq_speed_glm)

Call:
glm(formula = Speed_Diff ~ Freq * (Flow + Darkness + Ablation + 
    Flow:Ablation + Flow:Darkness), data = comp_data_freqs)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.58056  -0.14862  -0.03226   0.10369   1.67245  

Coefficients:
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       0.7069     0.0724   9.764   <2e-16 ***
Freq                             -2.2974     1.7766  -1.293   0.1977    
FlowFlow 2                        0.1974     0.1070   1.846   0.0667 .  
DarknessDark                     -0.2170     0.1176  -1.845   0.0668 .  
AblationAblated                   0.1003     0.1035   0.968   0.3342    
FlowFlow 2:AblationAblated       -0.3068     0.1521  -2.017   0.0453 *  
FlowFlow 2:DarknessDark           0.3467     0.1707   2.031   0.0438 *  
Freq:FlowFlow 2                  -1.3837     2.4277  -0.570   0.5694    
Freq:DarknessDark                 3.5412     2.9607   1.196   0.2333    
Freq:AblationAblated             -2.2364     2.4558  -0.911   0.3638    
Freq:FlowFlow 2:AblationAblated   4.7660     3.3948   1.404   0.1621    
Freq:FlowFlow 2:DarknessDark     -4.6976     4.0855  -1.150   0.2518    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.08537927)

    Null deviance: 18.369  on 183  degrees of freedom
Residual deviance: 14.685  on 172  degrees of freedom
AIC: 83

Number of Fisher Scoring iterations: 2

freq_heading_glm <- glm(Fold_Heading_Diff ~ Freq*(Flow+Darkness+Ablation+Flow:Ablation+Flow:Darkness), data = comp_data_freqs)

summary(freq_heading_glm)

Call:
glm(formula = Fold_Heading_Diff ~ Freq * (Flow + Darkness + Ablation + 
    Flow:Ablation + Flow:Darkness), data = comp_data_freqs)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-35.899   -4.374   -0.533    4.584   41.173  

Coefficients:
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       29.280      2.293  12.772  < 2e-16 ***
Freq                             105.736     56.256   1.880  0.06186 .  
FlowFlow 2                        16.080      3.387   4.748 4.31e-06 ***
DarknessDark                       7.954      3.724   2.136  0.03411 *  
AblationAblated                    8.450      3.278   2.578  0.01078 *  
FlowFlow 2:AblationAblated       -13.779      4.817  -2.861  0.00475 ** 
FlowFlow 2:DarknessDark          -16.857      5.406  -3.118  0.00213 ** 
Freq:FlowFlow 2                 -179.547     76.873  -2.336  0.02066 *  
Freq:DarknessDark                -60.112     93.753  -0.641  0.52227    
Freq:AblationAblated            -172.808     77.766  -2.222  0.02758 *  
Freq:FlowFlow 2:AblationAblated  279.733    107.498   2.602  0.01007 *  
Freq:FlowFlow 2:DarknessDark     304.057    129.368   2.350  0.01989 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 85.60996)

    Null deviance: 18576  on 183  degrees of freedom
Residual deviance: 14725  on 172  degrees of freedom
AIC: 1354.5

Number of Fisher Scoring iterations: 2

freq_sync_glm <- glm(Sync ~ Freq*(Flow+Darkness+Ablation+Flow:Ablation+Flow:Darkness), data = comp_data_freqs)

summary(freq_sync_glm)

Call:
glm(formula = Sync ~ Freq * (Flow + Darkness + Ablation + Flow:Ablation + 
    Flow:Darkness), data = comp_data_freqs)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.49785  -0.05122  -0.00219   0.05194   0.36839  

Coefficients:
                                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)                      0.5736663  0.0301319  19.039   <2e-16 ***
Freq                            -0.7636827  0.7394078  -1.033    0.303    
FlowFlow 2                       0.0008242  0.0445166   0.019    0.985    
DarknessDark                     0.1008135  0.0489509   2.059    0.041 *  
AblationAblated                 -0.0172332  0.0430865  -0.400    0.690    
FlowFlow 2:AblationAblated       0.0064293  0.0633081   0.102    0.919    
FlowFlow 2:DarknessDark         -0.1166197  0.0710527  -1.641    0.103    
Freq:FlowFlow 2                  0.3182002  1.0103926   0.315    0.753    
Freq:DarknessDark               -1.3454754  1.2322589  -1.092    0.276    
Freq:AblationAblated             0.3667070  1.0221233   0.359    0.720    
Freq:FlowFlow 2:AblationAblated -0.3483264  1.4129158  -0.247    0.806    
Freq:FlowFlow 2:DarknessDark     1.6647306  1.7003671   0.979    0.329    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 0.01478952)

    Null deviance: 2.7261  on 183  degrees of freedom
Residual deviance: 2.5438  on 172  degrees of freedom
AIC: -239.59

Number of Fisher Scoring iterations: 2

freq_speed_gam <- gam(Speed_Diff ~ s(Freq,by=Flow_Ablation_Darkness),
                              data = comp_data_freqs)

summary(freq_speed_gam)

Family: gaussian 
Link function: identity 

Formula:
Speed_Diff ~ s(Freq, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.65610    0.02396   27.39   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                           edf Ref.df     F p-value  
s(Freq):Flow_Ablation_DarknessFlow 0, Ablated, Light     1.369  1.645 3.648  0.0241 *
s(Freq):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  1.243  1.446 0.430  0.7141  
s(Freq):Flow_Ablation_DarknessFlow 0, No Ablation, Light 1.000  1.000 1.489  0.2240  
s(Freq):Flow_Ablation_DarknessFlow 2, Ablated, Light     1.000  1.000 0.457  0.4998  
s(Freq):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  8.018  8.330 2.528  0.0135 *
s(Freq):Flow_Ablation_DarknessFlow 2, No Ablation, Light 1.321  1.571 2.232  0.0801 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.114   Deviance explained = 18.2%
GCV = 0.096783  Scale est. = 0.08892   n = 184

freq_heading_gam <- gam(Fold_Heading_Diff ~ s(Freq,by=Flow_Ablation_Darkness),
                              data = comp_data_freqs)

summary(freq_heading_gam)

Family: gaussian 
Link function: identity 

Formula:
Fold_Heading_Diff ~ s(Freq, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  39.7569     0.7495   53.05   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                           edf Ref.df     F p-value    
s(Freq):Flow_Ablation_DarknessFlow 0, Ablated, Light     1.000  1.000 1.278 0.25978    
s(Freq):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  1.000  1.000 0.379 0.53893    
s(Freq):Flow_Ablation_DarknessFlow 0, No Ablation, Light 7.190  7.969 3.942 0.00028 ***
s(Freq):Flow_Ablation_DarknessFlow 2, Ablated, Light     1.391  1.677 0.300 0.59859    
s(Freq):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  1.000  1.000 6.038 0.01501 *  
s(Freq):Flow_Ablation_DarknessFlow 2, No Ablation, Light 1.000  1.000 1.688 0.19564    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =   0.15   Deviance explained = 20.8%
GCV = 93.207  Scale est. = 86.328    n = 184

freq_sync_gam <- gam(Sync ~ s(Freq,by=Flow_Ablation_Darkness),
                              data = comp_data_freqs)

summary(freq_sync_gam)

Family: gaussian 
Link function: identity 

Formula:
Sync ~ s(Freq, by = Flow_Ablation_Darkness)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.552151   0.009333   59.16   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
                                                           edf Ref.df     F p-value   
s(Freq):Flow_Ablation_DarknessFlow 0, Ablated, Light     1.000  1.000 0.328 0.56755   
s(Freq):Flow_Ablation_DarknessFlow 0, No Ablation, Dark  5.900  6.791 3.273 0.00286 **
s(Freq):Flow_Ablation_DarknessFlow 0, No Ablation, Light 2.973  3.709 1.168 0.26685   
s(Freq):Flow_Ablation_DarknessFlow 2, Ablated, Light     1.000  1.000 0.431 0.51217   
s(Freq):Flow_Ablation_DarknessFlow 2, No Ablation, Dark  1.000  1.000 0.017 0.89556   
s(Freq):Flow_Ablation_DarknessFlow 2, No Ablation, Light 1.000  1.000 0.436 0.51011   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.101   Deviance explained = 16.4%
GCV = 0.014483  Scale est. = 0.013391  n = 184

Now we make some predictions for this.

f <- seq(from = 0.005, to = 0.07, by = 0.001)

flows <- c("Flow 0", "Flow 2")
ablation <- c("No Ablation", "Ablated")
dark <- c("Light","Dark")

freq_predict_df <- expand.grid(Freq = f, Flow = flows, Ablation = ablation, Darkness = dark)

freq_predict_df <- freq_predict_df %>% mutate(Flow_Ablation_Darkness = factor(paste(Flow,Ablation,Darkness,sep=", "))) %>% 
                            filter(!(Ablation == "Ablated" & Darkness == 'Dark'))

freq_predict_df <- freq_predict_df %>% mutate(pred_speed_diff = predict.gam(freq_speed_gam,freq_predict_df),
                                    pred_heading_diff = predict.gam(freq_heading_gam,freq_predict_df),
                                    pred_sync = predict.gam(freq_sync_gam,freq_predict_df))

ggplot(comp_data_freqs, aes(x = Freq, y = Speed_Diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", formula = "y ~ x", se = FALSE) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Preference and Senses on Speed Difference") +
  xlab("Frequency of Observations") +
  ylab("Speed Difference (BL/s)") +
  theme_light()

ggplot(comp_data_freqs, aes(x = Freq, y = Fold_Heading_Diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", formula = "y ~ x", se = FALSE) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Preference and Senses on Heading Difference") +
  xlab("Frequency of Observations") +
  ylab("Heading Difference (Degrees)") +
  theme_light()

ggplot(comp_data_freqs, aes(x = Freq, y = Sync, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", formula = "y ~ x", se = FALSE) +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Preference and Senses on Synchonization") +
  xlab("Frequency of Observations") +
  ylab("Synchonization") +
  theme_light()

ggplot(freq_predict_df, aes(x = Freq, y = pred_speed_diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Frequency of Observations on Speed Difference") +
  xlab("Frequency (%)") +
  ylab("Speed Difference (BL/s)") +
  theme_light()

ggplot(freq_predict_df, aes(x = Freq, y = pred_heading_diff, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Frequency of Observations on Heading Difference") +
  xlab("Frequency (%)") +
  ylab("Heading Difference (Degrees)") +
  theme_light()

ggplot(freq_predict_df, aes(x = Freq, y = pred_sync, color = interaction(Ablation,Darkness,sep=", "),
                       fill = interaction(Ablation,Darkness,sep=", "))) +
  geom_line() +
  facet_wrap(~ Flow) +
  guides(fill = "none", color = guide_legend(title = "Condition")) +
  scale_color_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  scale_fill_manual(values=c("#000000", "#4CB944", "#00A7E1")) +
  ggtitle("Effect of Frequency of Observations on Synchonization") +
  xlab("Frequency (%)") +
  ylab("Synchonization") +
  theme_light()